Nuprl Lemma : add-remove-fresh-sq
∀I:Cname List. ([fresh-cname(I) / I]-[fresh-cname(I)] ~ I)
Proof
Definitions occuring in Statement :
fresh-cname: fresh-cname(I),
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
cons: [a / b],
nil: [],
list: T List,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
coordinate_name: Cname,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
add-remove-fresh-cname,
list_wf,
coordinate_name_wf,
subtype_base_sq,
list_subtype_base,
set_subtype_base,
le_wf,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
instantiate,
cumulativity,
independent_isectElimination,
sqequalRule,
intEquality,
lambdaEquality,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}I:Cname List. ([fresh-cname(I) / I]-[fresh-cname(I)] \msim{} I)
Date html generated:
2016_05_20-AM-09_28_49
Last ObjectModification:
2015_12_28-PM-04_48_06
Theory : cubical!sets
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