Nuprl Lemma : subst-frame-alpha
∀[opr:Type]. ∀t:term(opr). ∀s:(varname() × term(opr)) List. alpha-eq-terms(opr;subst-frame(s;t);t)
Proof
Definitions occuring in Statement :
subst-frame: subst-frame(s;t),
alpha-eq-terms: alpha-eq-terms(opr;a;b),
term: term(opr),
varname: varname(),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
subst-frame: subst-frame(s;t),
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
alpha-avoid-equivalent,
vars-of-subst_wf,
subtype_rel_list,
varname_wf,
not_wf,
equal-wf-T-base,
nullvar_wf,
istype-void,
vars-of-subst-not-nullvar,
list_wf,
term_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
applyEquality,
setEquality,
baseClosed,
independent_isectElimination,
lambdaEquality_alt,
setElimination,
rename,
setIsType,
universeIsType,
because_Cache,
sqequalRule,
functionIsType,
equalityIstype,
productEquality,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}t:term(opr). \mforall{}s:(varname() \mtimes{} term(opr)) List. alpha-eq-terms(opr;subst-frame(s;t);t)
Date html generated:
2020_05_19-PM-09_57_50
Last ObjectModification:
2020_03_09-PM-04_10_03
Theory : terms
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