Nuprl Lemma : isvarterm_functionality
∀[opr:Type]. ∀[t,t':term(opr)]. isvarterm(t) = isvarterm(t') supposing alpha-eq-terms(opr;t;t')
Proof
Definitions occuring in Statement :
alpha-eq-terms: alpha-eq-terms(opr;a;b),
isvarterm: isvarterm(t),
term: term(opr),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
true: True,
isvarterm: isvarterm(t),
isl: isl(x),
varterm: varterm(v),
btrue: tt,
squash: ↓T,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
false: False,
alpha-eq-terms: alpha-eq-terms(opr;a;b),
alpha-aux: alpha-aux(opr;vs;ws;a;b),
mkterm: mkterm(opr;bts),
bfalse: ff
Lemmas referenced :
term-cases,
alpha-eq-terms_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
btrue_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
isvarterm_wf,
term_wf,
subtype_rel_self,
iff_weakening_equal,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
unionElimination,
hypothesis,
universeIsType,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
because_Cache,
productElimination,
instantiate,
cumulativity,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
natural_numberEquality,
applyEquality,
lambdaEquality_alt,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
voidElimination,
hyp_replacement
Latex:
\mforall{}[opr:Type]. \mforall{}[t,t':term(opr)]. isvarterm(t) = isvarterm(t') supposing alpha-eq-terms(opr;t;t')
Date html generated:
2020_05_19-PM-09_55_51
Last ObjectModification:
2020_05_13-PM-03_40_27
Theory : terms
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