Nuprl Lemma : PFan_wf
PFan{i:l}() ∈ ℙ'
Proof
Definitions occuring in Statement :
PFan: PFan{i:l}(),
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
PFan: PFan{i:l}(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s],
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
nat_wf,
list_wf,
bool_wf,
decidable_wf,
iseg_wf,
not_wf,
equal_wf,
map_wf,
int_seg_wf,
int_seg_subtype_nat,
false_wf,
pi1_wf,
upto_wf,
pi2_wf,
exists_wf,
subtype_rel_dep_function,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
functionEquality,
productEquality,
because_Cache,
functionExtensionality,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
productElimination,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
PFan\{i:l\}() \mmember{} \mBbbP{}'
Date html generated:
2017_04_17-AM-09_39_10
Last ObjectModification:
2017_02_27-PM-05_35_54
Theory : fan-theorem
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