Nuprl Lemma : equiv-substs_wf
∀[opr:Type]. ∀[s1,s2:(varname() × term(opr)) List]. (equiv-substs(opr;s1;s2) ∈ ℙ)
Proof
Definitions occuring in Statement :
equiv-substs: equiv-substs(opr;s1;s2),
term: term(opr),
varname: varname(),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equiv-substs: equiv-substs(opr;s1;s2),
prop: ℙ,
all: ∀x:A. B[x],
and: P ∧ Q,
implies: P ⇒ Q,
isl: isl(x),
outl: outl(x),
uimplies: b supposing a,
not: ¬A,
false: False
Lemmas referenced :
varname_wf,
equal_wf,
bool_wf,
apply-alist_wf,
var-deq_wf,
term_wf,
btrue_wf,
bfalse_wf,
assert_wf,
alpha-eq-terms_wf,
assert_elim,
btrue_neq_bfalse,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
hypothesis,
productEquality,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
independent_isectElimination,
dependent_set_memberEquality_alt,
independent_pairFormation,
productIsType,
applyLambdaEquality,
setElimination,
rename,
productElimination,
voidElimination,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[s1,s2:(varname() \mtimes{} term(opr)) List]. (equiv-substs(opr;s1;s2) \mmember{} \mBbbP{})
Date html generated:
2020_05_19-PM-09_57_35
Last ObjectModification:
2020_03_09-PM-04_09_52
Theory : terms
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