Nuprl Lemma : function-eq_wf_type_function
∀A:Type. ∀B:type-function{i:l}(A). ∀f,g:Base. (function-eq(A;a.B[a];f;g) ∈ Type)
Proof
Definitions occuring in Statement :
type-function: type-function{i:l}(A),
function-eq: function-eq(A;a.B[a];f;g),
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
function-eq: function-eq(A;a.B[a];f;g),
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
type-function_wf,
equal-wf-base,
isect_wf,
base_wf,
uall_wf,
per-function-type-apply
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
baseApply,
closedConclusion,
baseClosed,
universeEquality
Latex:
\mforall{}A:Type. \mforall{}B:type-function\{i:l\}(A). \mforall{}f,g:Base. (function-eq(A;a.B[a];f;g) \mmember{} Type)
Date html generated:
2016_05_13-PM-03_53_48
Last ObjectModification:
2016_01_14-PM-07_15_40
Theory : per!type
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