Nuprl Rule : hyp_replacement

This rule proved as lemma rule_hyp_replacement_true3 in file rules_equality7.v at https://github.com/vrahli/NuprlInCoq

This is the rule that states that types are extensional.
If A is provably equal to B in ⌜Type⌝ then we can replace hypothesis x:A
by hypothesis x:B.
In particular, from x:B we have ⌜x ∈ B⌝ and therefore ⌜x ∈ A⌝.⋅

H x:A, J ⊢ C ext t

  BY hyp_replacement #$j B !parameter{i:l} ()

  H x:B, J ⊢ C ext t
  H x:A, J ⊢ A = B ∈ Type

Definitions occuring in rule : equal: s = t ∈ T, universe: Type, axiom: Ax

Latex:
H x:A, J \mvdash{} C ext t BY hyp\_replacement \#\$j B !parameter\{i:l\} () H x:B, J \mvdash{} C ext t H x:A, J \mvdash{} A = B Date html generated: 2019_06_20-PM-04_11_46 Last ObjectModification: 2016_07_09-PM-04_22_33 Theory : rules Home Index