Nuprl Lemma : equiv-substs-equiv-rel
∀[opr:Type]. EquivRel((varname() × term(opr)) List;s1,s2.equiv-substs(opr;s1;s2))
Proof
Definitions occuring in Statement :
equiv-substs: equiv-substs(opr;s1;s2),
term: term(opr),
varname: varname(),
list: T List,
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
equiv-substs: equiv-substs(opr;s1;s2),
cand: A c∧ B,
implies: P ⇒ Q,
isl: isl(x),
sym: Sym(T;x,y.E[x; y]),
prop: ℙ,
trans: Trans(T;x,y.E[x; y]),
guard: {T},
outl: outl(x),
uimplies: b supposing a,
not: ¬A,
false: False
Lemmas referenced :
alpha-eq-equiv-rel,
apply-alist_wf,
varname_wf,
var-deq_wf,
term_wf,
btrue_wf,
bfalse_wf,
istype-assert,
list_wf,
equiv-substs_wf,
istype-universe,
assert_elim,
btrue_neq_bfalse,
assert_wf,
equal_wf,
bool_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
independent_pairFormation,
lambdaFormation_alt,
inhabitedIsType,
unionElimination,
sqequalRule,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
universeIsType,
productEquality,
instantiate,
universeEquality,
independent_isectElimination,
dependent_set_memberEquality_alt,
productIsType,
applyLambdaEquality,
setElimination,
rename,
voidElimination,
hyp_replacement
Latex:
\mforall{}[opr:Type]. EquivRel((varname() \mtimes{} term(opr)) List;s1,s2.equiv-substs(opr;s1;s2))
Date html generated:
2020_05_19-PM-09_57_38
Last ObjectModification:
2020_03_09-PM-04_09_54
Theory : terms
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